Mathematical Biosciences and Engineering, 2014, 11(5): 1175-1180. doi: 10.3934/mbe.2014.11.1175

Primary: 34K20, 92D30; Secondary: 34D23.

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Disease dynamics for the hometown of migrant workers

1. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario

A recent paper by L. Wang, X. Wang J. Theoret. Biol. 300:100--109 (2012) formulatedand studied a delay differential equation model for disease dynamics in a region where a portionof the population leaves to work in a different region for an extended fixed period. Upon return,a fraction of the migrant workers have become infected with the disease.The global dynamics were not fully resolved in that paper, but are resolved here. We show thatfor all parameter values and all delays, the unique equilibrium is globally asymptotically stable,implying that the disease will eventually reach a constant positive level in the population.
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